# Flow over a 2D hill

Authors: Almeida et al.

Type: Experimental

Status:

Description

## Description

Flows over 2D polynomial-shaped obstacle(s) mounted on a flat plate with recirculation region in their wake.

In the first configuration, case A, a single hill is mounted on the bottom of the channel. In the second one, case B, a periodic flow is achieved over a series of consecutive hills mounted at the same location. The channel height is H = 170 mm and the maximum height and length of each hill are respectively hmax = 28 mm and 2R = 108 mm. In the case of consecutive hills, the space between each of them is 4.5hmax.

The shape of the hills was to be the inverse of a fourth-order polynomial but the actual shape is a bit different. The actual values of the height h(x) of the two-dimensional hills are given by:

Between x=0. and x=9. h(x)=min(28., 2.800000000000E+01 +0.000000000000E+00*x +6.775070969851E-03*x^2 -2.124527775800E-03*x^3 )
Between x=9. and x=14. h(x)= 2.507355893131E+01 +9.754803562315E-01*x -1.016116352781E-01*x^2 +1.889794677828E-03*x^3
Between x=14. and x=20. h(x)= 2.579601052357E+01 +8.206693007457E-01*x -9.055370274339E-02*x^2 +1.626510569859E-03*x^3
Between x=20. and x=30. h(x)= 4.046435022819E+01 -1.379581654948E+00*x +1.945884504128E-02*x^2 -2.070318932190E-04*x^3
Between x=30. and x=40. h(x)= 1.792461334664E+01 +8.743920332081E-01*x -5.567361123058E-02*x^2 +6.277731764683E-04*x^3
Between x=40. and x=54. h(x)=max(0., 5.639011190988E+01 -2.010520359035E+00*x +1.644919857549E-02*x^2 +2.674976141766E-05*x^3 )

## Flow Parameters

The hills are located about 6 m downstream of the tunnel inlet where a fully-developed channel flow is achieved in the absence of the obstacle(s). In case A, the measurements have been made around a single hill and, in case B, between two consecutive hills (the 7th and the 8th) located within an array of 10 equally spaced hills. The flow separates in the region of unfavourable pressure gradient on the downstream surface of the hills and, in the case of multiple hills, reattaches at an oblique angle on the upstream surface of the next hill. Very high levels of velocity fluctuations have been measured in the shear layers surrounding the recirculation bubbles.

• Water with a kinematic viscosity: nu = 1×10-6 m2/s.
• Mean centreline velocity at inlet: Uo = 2.147 m/s.
• Reynolds number: Uo h/nu = 60,000.

The case was considered at the 4th ERCOFTAC/IAHR Workshop on Refined Flow Modelling, held at Karlsruhe in 1995.

The experimental data can be downloaded from the ERCOFTAC test case database:

• Hill description:

## Reference Publications

1. ALMEIDA, G.P., DURAO, D.F.G. & HEITOR, M.V. (1992). Wake flows behind two dimensional model hills. Exp. Thermal and Fluid Science, 7, p.87
2. ALMEIDA, G.P., DURAO, D.F.G., SIMOES J.P. & HEITOR, M.V. (1990). Laser-Doppler measurements of fully developed turbulent channel flow. Proc. 5th Symp. Appl Laser Techniques to Fluid Meet., pp. 5-12
3. SNYDER, W.H. & HUNT, J.C.R. (1980). Experiments on stably and neutrally stratified flow over a model three-dimensional hill. Journal Fluids Mechanics, Vol. 96, pp. 671-704
4. CASTRO, J.P. & HAQUE, A. (1987). The structure of a turbulent shear layer bounding a separation region. Journal Fluid Mechanics, Vol. 179, pp. 439-468

## Results

Simulation results available for this case:
Code Version Author Restrictions
Code_Saturne 1.4.0 Juan Uribe Main.None
Code_Saturne 2.0-beta2 J. Uribe AccessEDFGroup
Number of topics: 2

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Topic revision: r5 - 2011-11-02 - 09:08:53 - JuanUribe
CfdTm Web
06 Dec 2019

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